Warm the butter and olive oil in a medium skillet over medium-low heat. Once butter is melted, add the shallots and sauté until they are softened and translucent, about 5 minutes. Add the garlic to the pan and sauté until fragrant, about 30 seconds.

Pour the peas into the skillet and stir them well, until they are coated with butter and well mixed. Season peas with salt and pepper, then add the chicken broth to the pan. Cover the pan with a lid, turn the heat to low, and simmer until the peas are tender and bright green in color, about 3 minutes. Remove the pan from the heat and top the peas with freshly grated parmesan. Serve immediately while still hot.